Geolocation has gained considerable attention over the last decade due to the enormous potential in the technology and the significant challenges facing this area of research. Geolocation technology provides the fundamental basis for a myriad of location-enabled services in different applications such as locating personnel and objects in residential homes, guiding shoppers inside a mall, locating the elderly in nursing homes or locating firefighters inside burning buildings.
Extending the success of multilateration techniques used by outdoor GPS systems to urban and indoor environments faces fundamental challenges due to their unique propagation environments. Specifically systems that rely on time of arrival (TOA), time difference of arrival (TDOA) and angle of arrival (AOA) work on the assumption that a line of sight (LOS) channel is always available between the reference point and the mobile device. In urban and indoor environments the availability of LOS signals is not always guaranteed due to physical obstructions such as buildings, walls, elevator shafts, etc.
Specifically, NLOS introduces a positive bias to the distance estimation which causes significant localization errors. As a result geolocation in light of the NLOS problem faces considerable challenges that affect the reliability and accuracy of the positioning systems. It is therefore vital to be able to identify NLOS channels in real-time and mitigate their impact on location estimation in order to enable effective and robust geolocation systems.
The integration and utilization of location information in day-to-day applications will grow significantly over the next decade as the technology's accuracy evolves. Currently outdoor localization, thanks to the GPS technology, has revolutionized navigation-based applications running on automotive GPS enabled devices and smart phones. Applications range from guiding drivers to their destination and providing a point-by-point direction to the closest cinema or coffee shop.
The success of GPS (an outdoor only time-of-arrival (TOA) based localization technology) has been due to the reliability, availability of line-of-sight (LOS) and practical accuracy that the orbiting satellites covering the globe provide. Recently as the number of smart devices and mobile users increased significantly, the potential for new location-based services and challenges emerged.
The lucrative business opportunities of location-enabled services are not limited to outdoors. In fact the potential of indoor location-enabled services has been projected by different sources as an untapped multi-billion dollar industry [1]. The range of indoor applications touches every aspect of our lives: from tracking children in day-care centers, tracking elderly in nursing homes, to tracking inventories in warehouses, tracking medical devices in hospitals and tracking personnel in emergency/first responder applications (e.g. firefighters inside a building).
The major challenge facing this new emerging industry is fundamental to the environment where the devices are to be deployed. As the nature of the applications moved closer to the urban cities (high-rise buildings) and into indoor buildings and residences, the problem of GPS coverage has surfaced.
For non-survey based localization technologies (such as GPS), the position is typically achieved through ranging (distance estimation or angle estimation) to different reference points (RPs) with known coordinates. Position estimation then involves solving a set of non-linear equations or through geometric relations.
Geolocation technologies that depend on techniques such time of arrival (TOA), time difference of arrival (TDOA) and angle of arrival (AOA) require a clear LOS between the RPs (the orbiting satellites in the GPS) and the mobile device.
Even in Received Signal Strength (RSS) based systems the LOS/NLOS channel information can be valuable as the technique relies on a priori pathloss models that are unique in those conditions. As a result, as the applications move close to dense urban areas and indoor environments, the major challenge facing accurate localization is the non-line of sight (NLOS) propagation problem [2]. NLOS propagation causes significant errors/biases to distance/angle estimation between mobile devices which affects the localization accuracy directly.
A robust approach to this problem is to identify the condition of the channels and then integrate this information in a NLOS mitigation algorithm. FIG. 1 provides an overview of where the NLOS identification technique can be integrated. For typical wireless geolocation systems a mobile device relies on N RPs to estimate its own position using measured metrics such as TOA, TDOA, AOA and RSS to infer geometric relation. In the figure two of the N measured signals experience NLOS conditions. In traditional approaches all the measurements are assumed to be under the LOS and large positioning errors will occur due to the NLOS corrupted measurements. In NLOS identification enabled systems, it is possible to identify the “bad links” and incorporate that information in a NLOS mitigation algorithm to estimate the position more accurately.
As shown in FIG. 1(a), in wireless geolocation systems, some range measurements (links) experience NLOS propagation where the LOS path is obstructed by objects, walls, etc. In this example the links for signals s1 and s3 experience NLOS propagation. As shown in FIG. 1(b), in traditional GPS-like systems, all the measurements are treated equally in the position estimation 100 and the system is “channel-blind”. This results in large estimation errors when some of the links experience NLOS conditions and therefore create incompatible or skewed estimates of the position.
FIG. 1(c) shows an overview of a location system in which NLOS Identification/Mitigation is provided. In such a system, the range measurements are first passed through a NLOS Identification Algorithm 110. Once the “bad links” are identified then that information is incorporated in a NLOS Mitigation Algorithm 120 prior to Position Estimation 130 which can improve accuracy substantially. In the example of FIG. 1(a), the NLOS Identification Algorithm would identify signals S1 and s3 as NLOS signals and the impact of these signals on the position estimate would then be mitigated by the NLOS Mitigation Algorithm 120 before the position estimate is created based on the remaining signals.
NLOS identification involves inferring the state of the channel by examining some properties of the received signal. For example a received signal under NLOS might exhibit significantly higher power variations in time compared to signals in LOS condition and as a result it is possible to infer the state of the channel. This approach however is not robust since it does not exploit all the available information. In addition there are cases where the time variation of LOS and NLOS are similar and the identification becomes difficult.
A more robust approach is to infer the state of the channel by estimating and analyzing the Channel Impulse Response (CIR) which is a characterization of the multipath profile of the channel between a mobile device and a RP. The CIR essentially contains the “history” of how the multipath signals reflected, diffracted and combined at the receiver and as a result this information has a stronger correlation with the channel condition be it LOS or NLOS. The existing NLOS identification techniques in literature are generally divided into two main approaches: CIR based and non-CIR based identification techniques.
In non-CIR based techniques the identification is achieved without estimating the CIR. Instead, identification is achieved by either examining some characteristic of the received signal or by assessing the impact of NLOS on the position estimation (that usually combine identification and mitigation in one step).
The most popular non-CIR based technique is the binary hypothesis test based on the statistical information/behavior of the range measurements TOA, RSS, and AOA, or a combination of them in hybrid approaches. In [3] the NLOS identification is achieved by analyzing the statistics of the time measurements and devising a binary hypothesis test to infer the state of the channel. Then the identification results are further verified through the adoption of a residual analysis rank test. Here, the residual is defined as the difference between the measured range and the calculated range.
In [4], NLOS identification is achieved through constructing a binary generalized likelihood ratio test (GLRT) using the TOA/TDOA (timing) range measurements to distinguish between LOS and NLOS conditions. The technique assumes that both LOS and NLOS range measurements follow a Gaussian distribution; while this might be valid for LOS, the assumption is not valid for most NLOS conditions.
Building on this idea, the work in [5] proposes three different statistical techniques to identify NLOS conditions depending on the a priori NLOS statistical information. If NLOS errors are treated as outliers (low probability of occurrence—i.e. few of the observations are NLOS) it then they can be identified through skewness and kurtosis tests. For the cases where more frequent NLOS errors occur but with a statistical PDF that is non-Gaussian and completely unknown, then [5] proposes different statistical tests (such as the modified Shapiro-Wilk W and the Anderson-Darling A2) to infer if the sample came from a normal distribution or not. In the cases that statistical distribution of NLOS range measurement are known but the parameters of the distribution are unknown, then a GLRT to identify NLOS measurements is proposed.
In [6] NLOS identification is achieved through a hybrid TOA/RSS hypothesis test where the statistics of TOA range measurements are combined with pathloss models that characterize the RSS in LOS and NLOS. One weakness of this technique is the reliance on a priori pathloss models which vary in different areas and also lacks accuracy in their relation to distance. The work is further extended in [7] where NLOS identification based on AOA statistics is proposed.
A hybrid TOA/RSS technique for acoustic localization is also proposed in [8] where by comparing distance estimates obtained from TOA and RSS (attenuation model) measurements a decision on the condition of the channel is obtained. A similar technique was proposed in a U.S. patent application where the TOA estimates are combined with RSS (pathloss model) information in a Bayesian framework [9]. Specifically, the likelihood of the channel being NLOS is computed through the Bayes' equation but relying on a priori pathloss models and statistical relationship of the channel condition and distance. This identification method's weakness is its dependence on a priori pathloss models which can vary in different environments.
A non-parametric binary hypothesis NLOS identification technique is proposed in [10] which assume that the statistics of the NLOS errors are usually unknown. As a result the technique first approximates the distribution of the range measurements then a Kullback-Leibler distance metric is used to determine the distance between the distribution of the measurement and the distribution of a prior known measurement distribution such as Gaussian in LOS condition. One major weakness of these techniques is that they rely on the statistics of range error which in many occasions might not provide sufficient information to clearly distinguish between LOS and NLOS. Measurement and modeling of range measurements have revealed that the distribution in LOS and NLOS at a given fixed location can be modeled as Gaussian. The NLOS biases in a fixed location are constant (unknown-deterministic), as a result in some cases when the environment is quasi-stationary the two distributions might not have sufficient separation between them [11].
Another non-CIR based NLOS identification technique is based on inferring the channel condition by examining the statistics of the envelope of the received signal. The basic idea behind this approach is that the envelope of the received signal has different statistical behavior in LOS versus NLOS. Two envelope-based NLOS identification techniques are proposed in [12] that are based on examining the envelope of the received signal for cellular systems. The first is based on the idea that the fading statistics of the signal envelope in LOS follows a Rician distribution while in NLOS it follows a Rayleigh distribution and thus a hypothesis test can be devised. The second technique achieves NLOS identification through analyzing the level crossing rate and the average fade duration which are different in Rician (LOS) and Rayleigh (NLOS) channels. A similar approach has been proposed in [13] where the LOS/NLOS identification is achieved through hypothesis test on the Rician K factor.
In [14] frequency diversity was exploited in a non-CIR based NLOS identification technique which examined the behavior of TOA estimation on different UWB-OFDM sub-bands. Since the signal propagation is affected by the center frequency (higher frequencies causes more attenuation), then as the frequency increases the TOA estimation will vary significantly in NLOS conditions. Thus by examining the TOA estimation across different sub-bands it is possible to infer the state of the channel. By analyzing the variance of TOA estimation across different sub-bands, [14] verified through experimental measurements that NLOS channels can be identified by exploiting frequency diversity.
Another alternative non-CIR NLOS identification technique is grouped under identification through evaluation of the quality of position estimation where the NLOS channel problem is dealt with indirectly as compared to the techniques so far. Specifically the location is typically estimated and the residual of position estimates is computed to infer the existence of NLOS links. The author in [15] recognized that it can be difficult to rely on the statistics of range measurements to identify NLOS channels and as a result proposed a technique called the Residual Weighting Algorithm (Rwgh) that combines the identification and mitigation and alleviates the effect of NLOS. The technique is based on the concept that the residual of the position estimation is typically higher when there are NLOS range measurements involved in the localization process. The NLOS links are “identified” through a repeated procedure of calculating and analyzing the residual for different groups of links. The links resulting in highest residual imply that they are in NLOS. The technique's major weakness is the requirement for repeated computation of the position and residual through a combinatorial process.
In [16] a linear programming approach to the NLOS problem has been proposed for sensor networks where the identification is implicitly achieved. In [17] an alternative non-parametric approach to distance based localization is proposed where a triangular inequality property of the Euclidean space is exploited and a hypothesis test is employed to classify links as LOS or NLOS. In [18] a modified residual test is used to identify and mitigate NLOS problems in cellular systems. In many localization applications mobile devices will be moving and this dynamic information can be exploited to identify NLOS conditions. Specifically in [19] a sequential Fault Detection and Isolation (FDI) technique is proposed to jointly identify NLOS and track the mobile user. In addition an unscented Kalman filtering approach is further investigated to address the joint NLOS and tracking problems. Similar work has been proposed in [20] [21].
The non-CIR based techniques that have been introduced thus far have focused on examining the received signal which is a limited attribute of the multipath channel. Another more robust approach is to analyze the multipath information through estimating the CIR. The CIR is a representation of the multipath signal arrivals at the receiver. It has been verified through numerous measurement experiments [22], [23], [24], [25] that the CIR of LOS channels exhibit statistical properties that are distinct from NLOS channels. All the CIR-based NLOS identification techniques in literature follow a binary hypothesis test, but the difference lies in the adopted test metric. The major proposed test metrics in literature are ratio of multipath components (power and time), mean excess delay, multipath delay spread and very recently kurtosis.
In LOS channels it is well known that the first (direct arrival) signal is typically the strongest. However for NLOS channels the first arrival path is not always the strongest (due to attenuation of the signal traveling through obstacles) and as a result a simple CIR-based NLOS identification approach is to evaluate the ratio of the first path and the strongest path. Intuitively if the first path is the strongest path, then the ratio is 1 highlighting a LOS while a very low ratio indicates a NLOS condition. This technique was proposed by [26] and [27]. This approach has limited identification capabilities since it does not exploit all the information available in the CIR.
An alternative approach is to analyze higher order statistics of the CIR to infer the condition of the channel. Since the CIR is a realization of a random process then characterizing the statistics of this random variable can provide a better insight into the condition of the channel. Specifically, CIRs of LOS channels should exhibit different statistical properties compared to CIRs of NLOS channels.
One basic statistical metric that has been used is the mean excess delay which is the first moment of the CIR. Small excess delay value indicates a LOS channel and larger excess delay imply NLOS. An excess delay hypothesis test to identify NLOS channels was proposed in [28], [29] and [33]. An improved NLOS identification can be achieved using the RMS delay spread which is a second moment statistics of the CIR. In [28], [29], [30], [31], [32] and [33] the RMS delay spread metric was used in NLOS identification with varying degrees of success. One major weakness of the RMS delay spread as a NLOS identification metric is that the conditional distributions of the RMS delay spread in LOS and NLOS are “close” to each other—weak correlation to the condition. This means that a hypothesis test will result in significant misdetections (LOS identified as NLOS—higher probability in making an error in the identification process) and as a result the metric is not a robust indicator of the channel condition.
Recognizing this, [28], [29] proposed a NLOS identification technique based on the kurtosis of the measured CIR which is defined as the ratio of the fourth order moment of the data to the square of the second order moment or the variance. Alternatively it can be a measure of how peaked or flat the data is relative to a normal distribution. Measurement data typically show that LOS channels are more “peaked” compared to “flatter” NLOS channels and thus higher kurtosis values can indicate a LOS channel. However the results in [28] clearly show that there are cases where kurtosis cannot provide satisfactory identification and as a result it is further proposed to use joint metrics (combining mean excess delay, RMS delay spread and kurtosis) for the NLOS identification. By combining the different metrics in a joint statistic the approach in [28] increases the information available to the identification process and thus improves the performance. This indicates that metrics which contain “more” information exhibit better NLOS identification capabilities. Since the introduction of the kurtosis based NLOS identification by [28] several other researchers evaluated the effectiveness of the kurtosis metric [33], [34], and [35].
What is evident from the above references is that the robustness of NLOS identification relies on the robustness of the metric used. The non-CIR based approaches provide “coarse” identification compared to the CIR-based techniques since they rely on the statistics of range measurement and not the channel information. Within the CIR-based techniques it is also evident that the robustness of the metric improves with the order of the statistics of the CIR. In addition to being verified experimentally, this relationship holds true since higher order statistics of a random variable characterize the random variable more accurately.
The NLOS Problem
In a multipath environment, the transmitted signal undergoes reflections, attenuations and diffractions prior to arriving at the receiver. At the receiver, replicas of the transmitted signal arrive attenuated, phase shifted and time-delayed. The multipath signal is a combination of those multiple signal arrivals. Formally the received signal can be described as
                              r          ⁡                      (            t            )                          =                              ∑                          k              =              1                                      L              p                                ⁢                                    α              k                        ⁢                          ⅇ                              jϕ                k                                      ⁢                          s              ⁡                              (                                  t                  -                                      τ                    k                                                  )                                                                        (        1        )            where s(t) is the transmitted signal waveform, r(t) is the received waveform, where Lp is the number of MPCs, and ακ, φk and τk are amplitude, phase and propagation delay of the signal traveling the kth path, respectively. A more practical approach to analyzing the impact of multipath on localization is to analyze the CIR which is usually modeled as,
                              h          ⁡                      (            τ            )                          =                              ∑                          k              =              1                                      L              p                                ⁢                                    α              k                        ⁢                          ⅇ                              jϕ                k                                      ⁢                          δ              ⁡                              (                                  t                  -                                      τ                    k                                                  )                                                                        (        2        )            where δ(□) is the Dirac delta function [2].
FIG. 2 illustrates multipath propagation in three different characteristic environments: (a) Outdoor open space—single bounce model; (b) Urban propagation; and (c) Indoor propagation.
In LOS conditions, the direct path signal is the strongest and it is possible to estimate the distance fairly accurately. Multipath signals (especially in dense cluttered environment) tend to arrive fairly close to the direct path. If the inter-arrival time between the multipath components is much smaller than the time-domain resolution of the system (low bandwidth systems) then at the receiver the multiple signals will combine to create a new cluster. The TOA estimate (from the receiver's point of view) will then be the peak of the cluster.
In order to clarify this phenomenon FIG. 3 illustrates a CIR example and the resulting envelope. In the example of FIG. 3 there are 10 multipath components indicated by the vertical arrows. The first multipath component is the strongest and in this case it is the LOS or direct path. The multipath components arrive after the direct path arrive in close proximity to each other (because of the nature of the propagation environment). For this system, the multipath components arrive and combine (due to low time-domain resolution) and appear at the receiver as 4 multipath components (the overall envelope shown by the solid line). As a result the peaks of this curve will ultimately be detected as path arrivals. The first path arrival will be estimated as the LOS path and thus used for distance estimation. However, it is clear in this case that the actual TOA as shown by the first arriving signal is not equal to the estimated TOA as derived from the peak of the envelope. This difference in estimation is due to the multipath error.
For higher system bandwidths, the multipath error in LOS environments is usually smaller. For example, FIG. 4 illustrates a measured CIR for 200 MHz bandwidth in a typical LOS office environment. From FIG. 4 it can be seen that the Estimated TOA and the Expected TOA, differ only marginally.
Thus, TOA-based ranging error in LOS environments is attributed to both multipath and measurement noise. Let α1DP and τ1DP denote the direct path (DP) amplitude and propagation delay, respectively. The distance between the transmitter and the receiver is dDP=ν×τ1DP, where ν is the speed of signal propagation. In general, TOA-based ranging accuracy is determined by the ranging error which is defined as the difference between the estimated and the actual distance or,ε={circumflex over (d)}−d  (3)
In a general LOS multipath environment the mobile device will experience varying error behavior depending on the structure of the propagation environment and the system bandwidth. In LOS the distance estimate can be modeled by{circumflex over (d)}DP=dDP+εDP(ω)+ñ  (4)where εDP={tilde over (b)}m(ω) is a bias induced by the multipath and it is a function of the system bandwidth and ñ is a zero-mean additive measurement noise. Typically the multipath error is modeled in the spatial domain as a zero mean Gaussian random variable [37]. This means that an ensemble of LOS measurements in a given LOS environment will generally result in a Gaussian distribution.
In NLOS conditions, however, there is an obstruction in the path of the transmitter and receiver. Depending on the type of obstruction and the relative distances of the transmitter/receiver to the obstruction, the channel behavior (CIR) and ranging error can vary significantly.
There are two specific NLOS cases or conditions that occur in typical obstructed environments. These are illustrated schematically in FIG. 5.
The first is when the DP signal is attenuated but detected (albeit with weak SNR). This situation is illustrated in FIG. 5a and can arise naturally when the transmitter and receiver are separated by “light” obstructions such as a glass door, wooden door or sheet-rock thin walls. Indeed in this scenario TOA estimates can be obtained with good accuracy due to the detection of the DP signal.
The second NLOS case occurs when there is a “heavy” obstruction between the transmitter and receiver which attenuates the DP severely making it difficult for the receiver to detect it. This situation is illustrated in FIG. 5b. The first non-direct path (NDP) component is then used for TOA estimation. This results in a significant bias that corrupts the TOA estimation and ultimately the position estimate.
Thus the two NLOS conditions can be explicitly distinguished by the presence or absence of the DP: NLOS-DP and NLOS-NDP, respectively. For the receiver to detect the DP, the ratio of the strongest MPC to that of the DP given by
                              κ          1                =                              max            ⁡                          (                                                                                      α                    i                                                                                      i                  =                  1                                                  L                  p                                            )                                            α            DP                                              (        5        )            must be less than the receiver dynamic range κ and the power of the DP must be greater than the receiver sensitivity φ. These constraints are given by,κ1≦κ  (6a)PDP>φ  (6b)where PDP=20 log10(α1DP) It is possible then to categorize the conditions based on the following ranging states [11]. In the presence of the DP (NLOS-DP), both the constraints κ1≦κ and PDP>φ are met and the distance estimate is accurate yielding{circumflex over (d)}DPNLOS=dDP+εDPNLOS+ñ  (7a)εDPNLOS=bpd+{tilde over (b)}m(ω)  (7b)where {tilde over (b)}m is the zero-mean random bias induced by the multipath, bpd is the bias corresponding to the propagation delay experienced by the signal going through the obstruction and ñ is a zero-mean additive measurement noise. It has been shown that {tilde over (b)}m is indeed a function of the bandwidth and signal to noise ratio (SNR) [23], while bpd dependent on the medium of the obstacle.
In the absence of the DP (NLOS-NDP), the requirement κ1≧κ is not met and the DP is shadowed by heavier obstacle burying its power under the dynamic range of the receiver. Ranging can be achieved using the amplitude and propagation delay of first NDP component given by α1NDP and τ1NDP respectively; resulting in a longer distance dNDP=ν×τ1NDP where dNDP>dDP. In this situation, the ranging estimate experiences a larger error compared to the other two conditions (LOS and NLOS-DP). Emphasizing that ranging is achieved through the first arriving NDP component, the estimate is then given by{circumflex over (d)}NDPNLOS=dDP+εNDPNLOS+ñ  (8a)εNDPNLOS=bpd+bB+{tilde over (b)}m(ω)  (8b)where bB is a deterministic but spatially random (due to the unknown nature of the obstacle) additive bias representing the “loss” of the DP. Unlike the multipath biases, and similar to biases induced by propagation delay, the dependence of bB on the system bandwidth and SNR has its own limitations as reported in [23].
To further illustrate the two NLOS conditions, FIGS. 6 and 7 show results of CIR measurements in a typical office environment for the two situations discussed above. FIG. 6 shows a CIR measurement of a “light” NLOS channel (NLOS-DP); the DP is attenuated but can be detected as shown by the circular highlight. FIG. 7 shows a CIR measurement of a severe NLOS multipath channel (NLOS-NDP); the DP is not detected as shown by the circular highlight.
This sub-classification of NLOS conditions has not received significant attention in NLOS identification literature and almost all techniques propose a binary hypothesis test to distinguish between LOS and NLOS. By adopting this traditional “black” or “white” approach, there is a high probability of misclassifying NLOS conditions which reduces the robustness of NLOS identification and mitigation algorithms. As a result in this invention report we define three channel conditions (hypotheses): LOS, NLOS-DP and NLOS-NDP and later we will illustrate through results of experimental measurements that it is necessary to devise a ternary hypothesis test to identify the condition. The characterization of ranging error in different scenarios is summarized in Table 1.
TABLE 1Summary of TOA-based Ranging Error ConditionsLOSNLOS-DPNLOS-NDPDistance{circumflex over (d)}DP = dDP +{circumflex over (d)}DPNLOS = dDP +{circumflex over (d)}NDPNLOS = dDP +calculationεDP (ω) + ñεDPNLOS + ñεNDPNLOS + ñErrorεDP (ω) = {tilde over (b)}m (ω)εDPNLOS = bpd +εNDPNLOS = bpd +{tilde over (b)}m (ω)bB + {tilde over (b)}m (ω)CIRIllustrated inIllustrated inIllustrated inFIG. 8FIG. 6FIG. 7
In order to enable effective, robust and accurate geolocation systems that operate in different multipath environments, it is thus desirable to incorporate NLOS identification algorithms in the localization estimation process.
Location enabled technology has received considerable attention in the last decade mainly due to the potential of integrating the technology in smart devices. GPS-enabled mobile devices have proven a great success in outdoor (non-obstructed) environments where the technology is used to guide drivers to their destinations or support pedestrians as they walk through the city. As the technology moves closer to dense urban environments and especially indoors, the localization performance degrades significantly. The main challenge facing localization in harsh multipath environments (such as indoors) is the NLOS problem which introduces significant errors to the location estimation.
As a result in order to enable accurate localization in such environments NLOS identification and mitigation algorithms should be integrated in the localization process. The effectiveness of NLOS mitigation will depend on the robustness of the NLOS identification, which means that the techniques have to demonstrate a high probability of detection in order to enable accurate localization performance. Although there are several state of the art NLOS identification techniques, their robustness and effectiveness are limited.
Accordingly, an object of the present invention is to provide one or more NLOS identification algorithms which are robust and effective. A further object of the present invention is to provide a mobile device which can accurately determine its position in an NLOS environment.